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<div class="header">
  <div class="summary">
<a href="#enum-members">Enumerations</a> &#124;
<a href="#func-members">Functions</a>  </div>
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<div class="title">spatial Namespace Reference</div>  </div>
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<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="enum-members"></a>
Enumerations</h2></td></tr>
<tr class="memitem:acc851583f244f19d9ea07490e9328b51"><td class="memItemLeft" align="right" valign="top">enum &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51">JointType</a> { <a class="el" href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51a35fa8acd1b8b1beb23e6c2e24313570c">JointType::Prismatic</a>, 
<a class="el" href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51a358561ac4d41f41d479b7c54b19b639e">JointType::Revolute</a>, 
<a class="el" href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51a70739581ffec4f3db3f3fe5c0a309c3a">JointType::FloatingBase</a>, 
<a class="el" href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51af80a4ad87fee7c9fdc19b7769495fdb5">JointType::Nothing</a>
 }</td></tr>
<tr class="separator:acc851583f244f19d9ea07490e9328b51"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:acab0e3d82f9a5385d482b83f2ee88eb1"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:acab0e3d82f9a5385d482b83f2ee88eb1"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a217c4c7a22cd434b9700b183b07f1505">SXform</a>&lt; T &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#acab0e3d82f9a5385d482b83f2ee88eb1">spatialRotation</a> (<a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5">CoordinateAxis</a> axis, T theta)</td></tr>
<tr class="separator:acab0e3d82f9a5385d482b83f2ee88eb1"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:acd5568b97b640537ab22aaf458c73980"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:acd5568b97b640537ab22aaf458c73980"><td class="memTemplItemLeft" align="right" valign="top">auto&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#acd5568b97b640537ab22aaf458c73980">motionCrossMatrix</a> (const Eigen::MatrixBase&lt; T &gt; &amp;v)</td></tr>
<tr class="separator:acd5568b97b640537ab22aaf458c73980"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a261bcef5a53b2fb64a5c7370420a1275"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a261bcef5a53b2fb64a5c7370420a1275"><td class="memTemplItemLeft" align="right" valign="top">auto&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#a261bcef5a53b2fb64a5c7370420a1275">forceCrossMatrix</a> (const Eigen::MatrixBase&lt; T &gt; &amp;v)</td></tr>
<tr class="separator:a261bcef5a53b2fb64a5c7370420a1275"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a49f73699d3c57d07835e8ab61af3f34a"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a49f73699d3c57d07835e8ab61af3f34a"><td class="memTemplItemLeft" align="right" valign="top">auto&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#a49f73699d3c57d07835e8ab61af3f34a">motionCrossProduct</a> (const Eigen::MatrixBase&lt; T &gt; &amp;a, const Eigen::MatrixBase&lt; T &gt; &amp;b)</td></tr>
<tr class="separator:a49f73699d3c57d07835e8ab61af3f34a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a705e44e685fd39dbd6c1a9002ae9a344"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a705e44e685fd39dbd6c1a9002ae9a344"><td class="memTemplItemLeft" align="right" valign="top">auto&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#a705e44e685fd39dbd6c1a9002ae9a344">forceCrossProduct</a> (const Eigen::MatrixBase&lt; T &gt; &amp;a, const Eigen::MatrixBase&lt; T &gt; &amp;b)</td></tr>
<tr class="separator:a705e44e685fd39dbd6c1a9002ae9a344"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a30b33586f68f1f6b31718848914a90ca"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a30b33586f68f1f6b31718848914a90ca"><td class="memTemplItemLeft" align="right" valign="top">auto&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#a30b33586f68f1f6b31718848914a90ca">sxformToHomogeneous</a> (const Eigen::MatrixBase&lt; T &gt; &amp;X)</td></tr>
<tr class="separator:a30b33586f68f1f6b31718848914a90ca"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a39cbc59fb7656b397d13c5a52799bf22"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a39cbc59fb7656b397d13c5a52799bf22"><td class="memTemplItemLeft" align="right" valign="top">auto&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#a39cbc59fb7656b397d13c5a52799bf22">homogeneousToSXform</a> (const Eigen::MatrixBase&lt; T &gt; &amp;H)</td></tr>
<tr class="separator:a39cbc59fb7656b397d13c5a52799bf22"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae4a2145f3028087511b4f17c0152ec83"><td class="memTemplParams" colspan="2">template&lt;typename T , typename T2 &gt; </td></tr>
<tr class="memitem:ae4a2145f3028087511b4f17c0152ec83"><td class="memTemplItemLeft" align="right" valign="top">auto&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#ae4a2145f3028087511b4f17c0152ec83">createSXform</a> (const Eigen::MatrixBase&lt; T &gt; &amp;R, const Eigen::MatrixBase&lt; T2 &gt; &amp;r)</td></tr>
<tr class="separator:ae4a2145f3028087511b4f17c0152ec83"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:abdc3cd991206414d80d9f89be27e3633"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:abdc3cd991206414d80d9f89be27e3633"><td class="memTemplItemLeft" align="right" valign="top">auto&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#abdc3cd991206414d80d9f89be27e3633">rotationFromSXform</a> (const Eigen::MatrixBase&lt; T &gt; &amp;X)</td></tr>
<tr class="separator:abdc3cd991206414d80d9f89be27e3633"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aba5e712bd3844d2e6a57dcb071f3f0a5"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:aba5e712bd3844d2e6a57dcb071f3f0a5"><td class="memTemplItemLeft" align="right" valign="top">auto&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#aba5e712bd3844d2e6a57dcb071f3f0a5">translationFromSXform</a> (const Eigen::MatrixBase&lt; T &gt; &amp;X)</td></tr>
<tr class="separator:aba5e712bd3844d2e6a57dcb071f3f0a5"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af37757ee8ad4510df5478202a62c9502"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:af37757ee8ad4510df5478202a62c9502"><td class="memTemplItemLeft" align="right" valign="top">auto&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#af37757ee8ad4510df5478202a62c9502">invertSXform</a> (const Eigen::MatrixBase&lt; T &gt; &amp;X)</td></tr>
<tr class="separator:af37757ee8ad4510df5478202a62c9502"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae1f2e71c723cc6a785153b3c92a82e84"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:ae1f2e71c723cc6a785153b3c92a82e84"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a3d70f8eb9cf1855ca989f887a5543acc">SVec</a>&lt; T &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#ae1f2e71c723cc6a785153b3c92a82e84">jointMotionSubspace</a> (<a class="el" href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51">JointType</a> joint, <a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5">CoordinateAxis</a> axis)</td></tr>
<tr class="separator:ae1f2e71c723cc6a785153b3c92a82e84"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a6440807f3b1854b1708f49048331811a"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:a6440807f3b1854b1708f49048331811a"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#ae8ab6bd4079a5317297be5eeb331b1ca">Mat6</a>&lt; T &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#a6440807f3b1854b1708f49048331811a">jointXform</a> (<a class="el" href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51">JointType</a> joint, <a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5">CoordinateAxis</a> axis, T q)</td></tr>
<tr class="separator:a6440807f3b1854b1708f49048331811a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa7ac11b744e5fad0c1cbef41e3bb209f"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:aa7ac11b744e5fad0c1cbef41e3bb209f"><td class="memTemplItemLeft" align="right" valign="top"><a class="el" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a>&lt; typename T::Scalar &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#aa7ac11b744e5fad0c1cbef41e3bb209f">rotInertiaOfBox</a> (typename T::Scalar mass, const Eigen::MatrixBase&lt; T &gt; &amp;dims)</td></tr>
<tr class="separator:aa7ac11b744e5fad0c1cbef41e3bb209f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a95b2db654a989f56df5a8977a5be12d6"><td class="memTemplParams" colspan="2">template&lt;typename T , typename T2 &gt; </td></tr>
<tr class="memitem:a95b2db654a989f56df5a8977a5be12d6"><td class="memTemplItemLeft" align="right" valign="top">auto&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#a95b2db654a989f56df5a8977a5be12d6">spatialToLinearVelocity</a> (const Eigen::MatrixBase&lt; T &gt; &amp;v, const Eigen::MatrixBase&lt; T2 &gt; &amp;x)</td></tr>
<tr class="separator:a95b2db654a989f56df5a8977a5be12d6"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af4cad4343e60d07ebdb543fb9a121a67"><td class="memTemplParams" colspan="2">template&lt;typename T &gt; </td></tr>
<tr class="memitem:af4cad4343e60d07ebdb543fb9a121a67"><td class="memTemplItemLeft" align="right" valign="top">auto&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#af4cad4343e60d07ebdb543fb9a121a67">spatialToAngularVelocity</a> (const Eigen::MatrixBase&lt; T &gt; &amp;v)</td></tr>
<tr class="separator:af4cad4343e60d07ebdb543fb9a121a67"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a13df9ec1359ecd4150251eaae0895198"><td class="memTemplParams" colspan="2">template&lt;typename T , typename T2 &gt; </td></tr>
<tr class="memitem:a13df9ec1359ecd4150251eaae0895198"><td class="memTemplItemLeft" align="right" valign="top">auto&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#a13df9ec1359ecd4150251eaae0895198">spatialToLinearAcceleration</a> (const Eigen::MatrixBase&lt; T &gt; &amp;a, const Eigen::MatrixBase&lt; T2 &gt; &amp;v)</td></tr>
<tr class="separator:a13df9ec1359ecd4150251eaae0895198"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a791e1bf3407f16ee4157ff943ea824dc"><td class="memTemplParams" colspan="2">template&lt;typename T , typename T2 , typename T3 &gt; </td></tr>
<tr class="memitem:a791e1bf3407f16ee4157ff943ea824dc"><td class="memTemplItemLeft" align="right" valign="top">auto&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#a791e1bf3407f16ee4157ff943ea824dc">spatialToLinearAcceleration</a> (const Eigen::MatrixBase&lt; T &gt; &amp;a, const Eigen::MatrixBase&lt; T2 &gt; &amp;v, const Eigen::MatrixBase&lt; T3 &gt; &amp;x)</td></tr>
<tr class="separator:a791e1bf3407f16ee4157ff943ea824dc"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ab521121fc7af2392144a78003c100a10"><td class="memTemplParams" colspan="2">template&lt;typename T , typename T2 &gt; </td></tr>
<tr class="memitem:ab521121fc7af2392144a78003c100a10"><td class="memTemplItemLeft" align="right" valign="top">auto&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#ab521121fc7af2392144a78003c100a10">sXFormPoint</a> (const Eigen::MatrixBase&lt; T &gt; &amp;X, const Eigen::MatrixBase&lt; T2 &gt; &amp;p)</td></tr>
<tr class="separator:ab521121fc7af2392144a78003c100a10"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3b32f3f809891285d9f1a8cf3c7cd16e"><td class="memTemplParams" colspan="2">template&lt;typename T , typename T2 &gt; </td></tr>
<tr class="memitem:a3b32f3f809891285d9f1a8cf3c7cd16e"><td class="memTemplItemLeft" align="right" valign="top">auto&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../de/d1a/namespacespatial.html#a3b32f3f809891285d9f1a8cf3c7cd16e">forceToSpatialForce</a> (const Eigen::MatrixBase&lt; T &gt; &amp;<a class="el" href="../../dc/dd7/test__casadi_8cpp.html#ae20d7fba59865a21504b65cdb44cbfe5">f</a>, const Eigen::MatrixBase&lt; T2 &gt; &amp;p)</td></tr>
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</table>
<h2 class="groupheader">Enumeration Type Documentation</h2>
<a class="anchor" id="acc851583f244f19d9ea07490e9328b51"></a>
<div class="memitem">
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          <td class="memname">enum <a class="el" href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51">spatial::JointType</a></td>
        </tr>
      </table>
  </td>
  <td class="mlabels-right">
<span class="mlabels"><span class="mlabel">strong</span></span>  </td>
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</div><div class="memdoc">
<table class="fieldtable">
<tr><th colspan="2">Enumerator</th></tr><tr><td class="fieldname"><a class="anchor" id="acc851583f244f19d9ea07490e9328b51a35fa8acd1b8b1beb23e6c2e24313570c"></a>Prismatic&#160;</td><td class="fielddoc">
</td></tr>
<tr><td class="fieldname"><a class="anchor" id="acc851583f244f19d9ea07490e9328b51a358561ac4d41f41d479b7c54b19b639e"></a>Revolute&#160;</td><td class="fielddoc">
</td></tr>
<tr><td class="fieldname"><a class="anchor" id="acc851583f244f19d9ea07490e9328b51a70739581ffec4f3db3f3fe5c0a309c3a"></a>FloatingBase&#160;</td><td class="fielddoc">
</td></tr>
<tr><td class="fieldname"><a class="anchor" id="acc851583f244f19d9ea07490e9328b51af80a4ad87fee7c9fdc19b7769495fdb5"></a>Nothing&#160;</td><td class="fielddoc">
</td></tr>
</table>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00021">21</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;{ <a class="code" href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51a35fa8acd1b8b1beb23e6c2e24313570c">Prismatic</a>, <a class="code" href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51a358561ac4d41f41d479b7c54b19b639e">Revolute</a>, <a class="code" href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51a70739581ffec4f3db3f3fe5c0a309c3a">FloatingBase</a>, <a class="code" href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51af80a4ad87fee7c9fdc19b7769495fdb5">Nothing</a> };</div><div class="ttc" id="namespacespatial_html_acc851583f244f19d9ea07490e9328b51a70739581ffec4f3db3f3fe5c0a309c3a"><div class="ttname"><a href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51a70739581ffec4f3db3f3fe5c0a309c3a">spatial::JointType::FloatingBase</a></div></div>
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<h2 class="groupheader">Function Documentation</h2>
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template&lt;typename T , typename T2 &gt; </div>
      <table class="memname">
        <tr>
          <td class="memname">auto spatial::createSXform </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>R</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T2 &gt; &amp;&#160;</td>
          <td class="paramname"><em>r</em>&#160;</td>
        </tr>
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          <td>)</td>
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<p>Create spatial coordinate transformation from rotation and translation </p>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00140">140</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>

<p>References <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00096">ori::vectorToSkewMat()</a>, and <a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">ori::X</a>.</p>
<div class="fragment"><div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;                                                {</div><div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;  static_assert(T::ColsAtCompileTime == 3 &amp;&amp; T::RowsAtCompileTime == 3,</div><div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;                <span class="stringliteral">&quot;Must have 3x3 matrix&quot;</span>);</div><div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;  static_assert(T2::ColsAtCompileTime == 1 &amp;&amp; T2::RowsAtCompileTime == 3,</div><div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;                <span class="stringliteral">&quot;Must have 3x1 matrix&quot;</span>);</div><div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae8ab6bd4079a5317297be5eeb331b1ca">Mat6&lt;typename T::Scalar&gt;</a> <a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a> = <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae8ab6bd4079a5317297be5eeb331b1ca">Mat6&lt;typename T::Scalar&gt;::Zero</a>();</div><div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;  X.template topLeftCorner&lt;3, 3&gt;() = R;</div><div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;  X.template bottomRightCorner&lt;3, 3&gt;() = R;</div><div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;  X.template bottomLeftCorner&lt;3, 3&gt;() = -R * <a class="code" href="../../da/d9b/namespaceori.html#a153f2a76610f0c5524da3f8bf8fa4dfa">vectorToSkewMat</a>(r);</div><div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;  <span class="keywordflow">return</span> X;</div><div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_ae8ab6bd4079a5317297be5eeb331b1ca"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#ae8ab6bd4079a5317297be5eeb331b1ca">Mat6</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 6, 6 &gt; Mat6</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00070">cppTypes.h:70</a></div></div>
<div class="ttc" id="namespaceori_html_a153f2a76610f0c5524da3f8bf8fa4dfa"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a153f2a76610f0c5524da3f8bf8fa4dfa">ori::vectorToSkewMat</a></div><div class="ttdeci">Mat3&lt; typename T::Scalar &gt; vectorToSkewMat(const Eigen::MatrixBase&lt; T &gt; &amp;v)</div><div class="ttdef"><b>Definition:</b> <a href="../../d4/dfb/orientation__tools_8h_source.html#l00096">orientation_tools.h:96</a></div></div>
<div class="ttc" id="namespaceori_html_a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">ori::CoordinateAxis::X</a></div></div>
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          <td class="memname">auto spatial::forceCrossMatrix </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>v</em></td><td>)</td>
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<p>Compute spatial force cross product matrix. Prefer forceCrossProduct when possible </p>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00060">60</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>

<p>References <a class="el" href="../../dc/dd7/test__casadi_8cpp_source.html#l00202">f()</a>.</p>
<div class="fragment"><div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;                                                   {</div><div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae8ab6bd4079a5317297be5eeb331b1ca">Mat6&lt;typename T::Scalar&gt;</a> <a class="code" href="../../dc/dd7/test__casadi_8cpp.html#ae20d7fba59865a21504b65cdb44cbfe5">f</a>;</div><div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;  f &lt;&lt; 0, -v(2), v(1), 0, -v(5), v(4), v(2), 0, -v(0), v(5), 0, -v(3), -v(1),</div><div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;      v(0), 0, -v(4), v(3), 0, 0, 0, 0, 0, -v(2), v(1), 0, 0, 0, v(2), 0, -v(0),</div><div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;      0, 0, 0, -v(1), v(0), 0;</div><div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;  <span class="keywordflow">return</span> <a class="code" href="../../dc/dd7/test__casadi_8cpp.html#ae20d7fba59865a21504b65cdb44cbfe5">f</a>;</div><div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_ae8ab6bd4079a5317297be5eeb331b1ca"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#ae8ab6bd4079a5317297be5eeb331b1ca">Mat6</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 6, 6 &gt; Mat6</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00070">cppTypes.h:70</a></div></div>
<div class="ttc" id="test__casadi_8cpp_html_ae20d7fba59865a21504b65cdb44cbfe5"><div class="ttname"><a href="../../dc/dd7/test__casadi_8cpp.html#ae20d7fba59865a21504b65cdb44cbfe5">f</a></div><div class="ttdeci">MX f(const MX &amp;x, const MX &amp;u)</div><div class="ttdef"><b>Definition:</b> <a href="../../dc/dd7/test__casadi_8cpp_source.html#l00202">test_casadi.cpp:202</a></div></div>
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          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>a</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>b</em>&#160;</td>
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<p>Compute spatial force cross product. Faster than the matrix multiplication version </p>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00091">91</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;                                                    {</div><div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;  static_assert(T::ColsAtCompileTime == 1 &amp;&amp; T::RowsAtCompileTime == 6,</div><div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;                <span class="stringliteral">&quot;Must have 6x1 vector&quot;</span>);</div><div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a3d70f8eb9cf1855ca989f887a5543acc">SVec&lt;typename T::Scalar&gt;</a> mv;</div><div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;  mv &lt;&lt; b(2) * a(1) - b(1) * a(2) - b(4) * a(5) + b(5) * a(4),</div><div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;      b(0) * a(2) - b(2) * a(0) + b(3) * a(5) - b(5) * a(3),</div><div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;      b(1) * a(0) - b(0) * a(1) - b(3) * a(4) + b(4) * a(3),</div><div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;      b(5) * a(1) - b(4) * a(2), b(3) * a(2) - b(5) * a(0),</div><div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;      b(4) * a(0) - b(3) * a(1);</div><div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;  <span class="keywordflow">return</span> mv;</div><div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a3d70f8eb9cf1855ca989f887a5543acc"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a3d70f8eb9cf1855ca989f887a5543acc">SVec</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 6, 1 &gt; SVec</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00062">cppTypes.h:62</a></div></div>
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          <td class="memname">auto spatial::forceToSpatialForce </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>f</em>, </td>
        </tr>
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          <td class="paramkey"></td>
          <td></td>
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          <td class="paramname"><em>p</em>&#160;</td>
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<p>Convert a force at a point to a spatial force </p><dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">f</td><td>: force </td></tr>
    <tr><td class="paramname">p</td><td>: point </td></tr>
  </table>
  </dd>
</dl>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00348">348</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;                                                       {</div><div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;  static_assert(T::ColsAtCompileTime == 1 &amp;&amp; T::RowsAtCompileTime == 3,</div><div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;                <span class="stringliteral">&quot;Must have 3x1 vector&quot;</span>);</div><div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;  static_assert(T2::ColsAtCompileTime == 1 &amp;&amp; T2::RowsAtCompileTime == 3,</div><div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;                <span class="stringliteral">&quot;Must have 3x1 vector&quot;</span>);</div><div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a3d70f8eb9cf1855ca989f887a5543acc">SVec&lt;typename T::Scalar&gt;</a> fs;</div><div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;  fs.template topLeftCorner&lt;3, 1&gt;() = p.cross(<a class="code" href="../../dc/dd7/test__casadi_8cpp.html#ae20d7fba59865a21504b65cdb44cbfe5">f</a>);</div><div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;  fs.template bottomLeftCorner&lt;3, 1&gt;() = <a class="code" href="../../dc/dd7/test__casadi_8cpp.html#ae20d7fba59865a21504b65cdb44cbfe5">f</a>;</div><div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;  <span class="keywordflow">return</span> fs;</div><div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a3d70f8eb9cf1855ca989f887a5543acc"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a3d70f8eb9cf1855ca989f887a5543acc">SVec</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 6, 1 &gt; SVec</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00062">cppTypes.h:62</a></div></div>
<div class="ttc" id="test__casadi_8cpp_html_ae20d7fba59865a21504b65cdb44cbfe5"><div class="ttname"><a href="../../dc/dd7/test__casadi_8cpp.html#ae20d7fba59865a21504b65cdb44cbfe5">f</a></div><div class="ttdeci">MX f(const MX &amp;x, const MX &amp;u)</div><div class="ttdef"><b>Definition:</b> <a href="../../dc/dd7/test__casadi_8cpp_source.html#l00202">test_casadi.cpp:202</a></div></div>
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          <td class="memname">auto spatial::homogeneousToSXform </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
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<p>Convert a homogeneous coordinate transformation to a spatial one </p>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00124">124</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>

<p>References <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00096">ori::vectorToSkewMat()</a>, and <a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">ori::X</a>.</p>
<div class="fragment"><div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;                                                      {</div><div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;  static_assert(T::ColsAtCompileTime == 4 &amp;&amp; T::RowsAtCompileTime == 4,</div><div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;                <span class="stringliteral">&quot;Must have 4x4 matrix&quot;</span>);</div><div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3&lt;typename T::Scalar&gt;</a> R = H.template topLeftCorner&lt;3, 3&gt;();</div><div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> translate = H.template topRightCorner&lt;3, 1&gt;();</div><div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae8ab6bd4079a5317297be5eeb331b1ca">Mat6&lt;typename T::Scalar&gt;</a> <a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a> = <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae8ab6bd4079a5317297be5eeb331b1ca">Mat6&lt;typename T::Scalar&gt;::Zero</a>();</div><div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;  X.template topLeftCorner&lt;3, 3&gt;() = R;</div><div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;  X.template bottomLeftCorner&lt;3, 3&gt;() = <a class="code" href="../../da/d9b/namespaceori.html#a153f2a76610f0c5524da3f8bf8fa4dfa">vectorToSkewMat</a>(translate) * R;</div><div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;  X.template bottomRightCorner&lt;3, 3&gt;() = R;</div><div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;  <span class="keywordflow">return</span> X;</div><div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_ae8ab6bd4079a5317297be5eeb331b1ca"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#ae8ab6bd4079a5317297be5eeb331b1ca">Mat6</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 6, 6 &gt; Mat6</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00070">cppTypes.h:70</a></div></div>
<div class="ttc" id="cpp_types_8h_html_aa8cb424e643d476ea485238dad7c3e18"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 3 &gt; Mat3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00054">cppTypes.h:54</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
<div class="ttc" id="namespaceori_html_a153f2a76610f0c5524da3f8bf8fa4dfa"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a153f2a76610f0c5524da3f8bf8fa4dfa">ori::vectorToSkewMat</a></div><div class="ttdeci">Mat3&lt; typename T::Scalar &gt; vectorToSkewMat(const Eigen::MatrixBase&lt; T &gt; &amp;v)</div><div class="ttdef"><b>Definition:</b> <a href="../../d4/dfb/orientation__tools_8h_source.html#l00096">orientation_tools.h:96</a></div></div>
<div class="ttc" id="namespaceori_html_a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">ori::CoordinateAxis::X</a></div></div>
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          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>X</em></td><td>)</td>
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<p>Invert a spatial transformation (much faster than matrix inverse) </p>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00181">181</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>

<p>References <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00140">createSXform()</a>, <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00108">ori::matToSkewVec()</a>, and <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00157">rotationFromSXform()</a>.</p>
<div class="fragment"><div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;                                               {</div><div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;  static_assert(T::ColsAtCompileTime == 6 &amp;&amp; T::RowsAtCompileTime == 6,</div><div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;                <span class="stringliteral">&quot;Must have 6x6 matrix&quot;</span>);</div><div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a0b83d93a3c74d282558436e26c056896">RotMat&lt;typename T::Scalar&gt;</a> R = <a class="code" href="../../de/d1a/namespacespatial.html#abdc3cd991206414d80d9f89be27e3633">rotationFromSXform</a>(X);</div><div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> r =</div><div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;      -<a class="code" href="../../da/d9b/namespaceori.html#a0d9277fde185aecf3eae4a6d6450d25f">matToSkewVec</a>(R.transpose() * <a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>.template bottomLeftCorner&lt;3, 3&gt;());</div><div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a217c4c7a22cd434b9700b183b07f1505">SXform&lt;typename T::Scalar&gt;</a> Xinv = <a class="code" href="../../de/d1a/namespacespatial.html#ae4a2145f3028087511b4f17c0152ec83">createSXform</a>(R.transpose(), -R * r);</div><div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;  <span class="keywordflow">return</span> Xinv;</div><div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a217c4c7a22cd434b9700b183b07f1505"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a217c4c7a22cd434b9700b183b07f1505">SXform</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 6, 6 &gt; SXform</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00066">cppTypes.h:66</a></div></div>
<div class="ttc" id="namespacespatial_html_ae4a2145f3028087511b4f17c0152ec83"><div class="ttname"><a href="../../de/d1a/namespacespatial.html#ae4a2145f3028087511b4f17c0152ec83">spatial::createSXform</a></div><div class="ttdeci">auto createSXform(const Eigen::MatrixBase&lt; T &gt; &amp;R, const Eigen::MatrixBase&lt; T2 &gt; &amp;r)</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/dc8/spatial_8h_source.html#l00140">spatial.h:140</a></div></div>
<div class="ttc" id="namespaceori_html_a0d9277fde185aecf3eae4a6d6450d25f"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a0d9277fde185aecf3eae4a6d6450d25f">ori::matToSkewVec</a></div><div class="ttdeci">Vec3&lt; typename T::Scalar &gt; matToSkewVec(const Eigen::MatrixBase&lt; T &gt; &amp;m)</div><div class="ttdef"><b>Definition:</b> <a href="../../d4/dfb/orientation__tools_8h_source.html#l00108">orientation_tools.h:108</a></div></div>
<div class="ttc" id="namespaceori_html_a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">ori::CoordinateAxis::X</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a0b83d93a3c74d282558436e26c056896"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a0b83d93a3c74d282558436e26c056896">RotMat</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 3 &gt; RotMat</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00018">cppTypes.h:18</a></div></div>
<div class="ttc" id="namespacespatial_html_abdc3cd991206414d80d9f89be27e3633"><div class="ttname"><a href="../../de/d1a/namespacespatial.html#abdc3cd991206414d80d9f89be27e3633">spatial::rotationFromSXform</a></div><div class="ttdeci">auto rotationFromSXform(const Eigen::MatrixBase&lt; T &gt; &amp;X)</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/dc8/spatial_8h_source.html#l00157">spatial.h:157</a></div></div>
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          <td class="memname"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a3d70f8eb9cf1855ca989f887a5543acc">SVec</a>&lt;T&gt; spatial::jointMotionSubspace </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51">JointType</a>&#160;</td>
          <td class="paramname"><em>joint</em>, </td>
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          <td class="paramtype"><a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5">CoordinateAxis</a>&#160;</td>
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<p>Compute joint motion subspace vector </p>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00195">195</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>

<p>References <a class="el" href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51a35fa8acd1b8b1beb23e6c2e24313570c">Prismatic</a>, and <a class="el" href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51a358561ac4d41f41d479b7c54b19b639e">Revolute</a>.</p>
<div class="fragment"><div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;                                                                  {</div><div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;T&gt;</a> v(0, 0, 0);</div><div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a3d70f8eb9cf1855ca989f887a5543acc">SVec&lt;T&gt;</a> phi = <a class="code" href="../../d9/d8e/cpp_types_8h.html#a3d70f8eb9cf1855ca989f887a5543acc">SVec&lt;T&gt;::Zero</a>();</div><div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;  <span class="keywordflow">if</span> (axis == CoordinateAxis::X)</div><div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;    v(0) = 1;</div><div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (axis == CoordinateAxis::Y)</div><div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;    v(1) = 1;</div><div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;  <span class="keywordflow">else</span></div><div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;    v(2) = 1;</div><div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;</div><div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;  <span class="keywordflow">if</span> (joint == JointType::Prismatic)</div><div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    phi.template bottomLeftCorner&lt;3, 1&gt;() = v;</div><div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (joint == JointType::Revolute)</div><div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;    phi.template topLeftCorner&lt;3, 1&gt;() = v;</div><div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;  <span class="keywordflow">else</span></div><div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;    <span class="keywordflow">throw</span> std::runtime_error(<span class="stringliteral">&quot;Unknown motion subspace&quot;</span>);</div><div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;</div><div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;  <span class="keywordflow">return</span> phi;</div><div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a3d70f8eb9cf1855ca989f887a5543acc"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a3d70f8eb9cf1855ca989f887a5543acc">SVec</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 6, 1 &gt; SVec</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00062">cppTypes.h:62</a></div></div>
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          <td class="memname"><a class="el" href="../../d9/d8e/cpp_types_8h.html#ae8ab6bd4079a5317297be5eeb331b1ca">Mat6</a>&lt;T&gt; spatial::jointXform </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51">JointType</a>&#160;</td>
          <td class="paramname"><em>joint</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype"><a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5">CoordinateAxis</a>&#160;</td>
          <td class="paramname"><em>axis</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">T&#160;</td>
          <td class="paramname"><em>q</em>&#160;</td>
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          <td></td>
          <td>)</td>
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<p>Compute joint transformation </p>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00219">219</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>

<p>References <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00140">createSXform()</a>, <a class="el" href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51a35fa8acd1b8b1beb23e6c2e24313570c">Prismatic</a>, <a class="el" href="../../de/d1a/namespacespatial.html#acc851583f244f19d9ea07490e9328b51a358561ac4d41f41d479b7c54b19b639e">Revolute</a>, <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00028">spatialRotation()</a>, and <a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">ori::X</a>.</p>
<div class="fragment"><div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;                                                              {</div><div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae8ab6bd4079a5317297be5eeb331b1ca">Mat6&lt;T&gt;</a> <a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a> = <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae8ab6bd4079a5317297be5eeb331b1ca">Mat6&lt;T&gt;::Zero</a>();</div><div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;  <span class="keywordflow">if</span> (joint == JointType::Revolute) {</div><div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;    X = <a class="code" href="../../de/d1a/namespacespatial.html#acab0e3d82f9a5385d482b83f2ee88eb1">spatialRotation</a>(axis, q);</div><div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (joint == JointType::Prismatic) {</div><div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;    <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;T&gt;</a> v(0, 0, 0);</div><div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;    <span class="keywordflow">if</span> (axis == CoordinateAxis::X)</div><div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;      v(0) = q;</div><div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (axis == CoordinateAxis::Y)</div><div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;      v(1) = q;</div><div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (axis == CoordinateAxis::Z)</div><div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;      v(2) = q;</div><div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;</div><div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;    X = <a class="code" href="../../de/d1a/namespacespatial.html#ae4a2145f3028087511b4f17c0152ec83">createSXform</a>(<a class="code" href="../../d9/d8e/cpp_types_8h.html#a0b83d93a3c74d282558436e26c056896">RotMat&lt;T&gt;::Identity</a>(), v);</div><div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;  } <span class="keywordflow">else</span> {</div><div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;    <span class="keywordflow">throw</span> std::runtime_error(<span class="stringliteral">&quot;Unknown joint xform\n&quot;</span>);</div><div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;  }</div><div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;  <span class="keywordflow">return</span> X;</div><div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_ae8ab6bd4079a5317297be5eeb331b1ca"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#ae8ab6bd4079a5317297be5eeb331b1ca">Mat6</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 6, 6 &gt; Mat6</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00070">cppTypes.h:70</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
<div class="ttc" id="namespacespatial_html_acab0e3d82f9a5385d482b83f2ee88eb1"><div class="ttname"><a href="../../de/d1a/namespacespatial.html#acab0e3d82f9a5385d482b83f2ee88eb1">spatial::spatialRotation</a></div><div class="ttdeci">SXform&lt; T &gt; spatialRotation(CoordinateAxis axis, T theta)</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/dc8/spatial_8h_source.html#l00028">spatial.h:28</a></div></div>
<div class="ttc" id="namespacespatial_html_ae4a2145f3028087511b4f17c0152ec83"><div class="ttname"><a href="../../de/d1a/namespacespatial.html#ae4a2145f3028087511b4f17c0152ec83">spatial::createSXform</a></div><div class="ttdeci">auto createSXform(const Eigen::MatrixBase&lt; T &gt; &amp;R, const Eigen::MatrixBase&lt; T2 &gt; &amp;r)</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/dc8/spatial_8h_source.html#l00140">spatial.h:140</a></div></div>
<div class="ttc" id="namespaceori_html_a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">ori::CoordinateAxis::X</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a0b83d93a3c74d282558436e26c056896"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a0b83d93a3c74d282558436e26c056896">RotMat</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 3 &gt; RotMat</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00018">cppTypes.h:18</a></div></div>
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          <td class="memname">auto spatial::motionCrossMatrix </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>v</em></td><td>)</td>
          <td></td>
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<p>Compute the spatial motion cross product matrix. Prefer motionCrossProduct when possible. </p>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00043">43</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;                                                    {</div><div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;  static_assert(T::ColsAtCompileTime == 1 &amp;&amp; T::RowsAtCompileTime == 6,</div><div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;                <span class="stringliteral">&quot;Must have 6x1 vector&quot;</span>);</div><div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#ae8ab6bd4079a5317297be5eeb331b1ca">Mat6&lt;typename T::Scalar&gt;</a> m;</div><div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;  m &lt;&lt; 0, -v(2), v(1), 0, 0, 0, v(2), 0, -v(0), 0, 0, 0, -v(1), v(0), 0, 0, 0,</div><div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;      0,</div><div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;</div><div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;      0, -v(5), v(4), 0, -v(2), v(1), v(5), 0, -v(3), v(2), 0, -v(0), -v(4),</div><div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;      v(3), 0, -v(1), v(0), 0;</div><div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;  <span class="keywordflow">return</span> m;</div><div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_ae8ab6bd4079a5317297be5eeb331b1ca"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#ae8ab6bd4079a5317297be5eeb331b1ca">Mat6</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 6, 6 &gt; Mat6</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00070">cppTypes.h:70</a></div></div>
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          <td class="memname">auto spatial::motionCrossProduct </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>a</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>b</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
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<p>Compute spatial motion cross product. Faster than the matrix multiplication version </p>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00073">73</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;                                                     {</div><div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;  static_assert(T::ColsAtCompileTime == 1 &amp;&amp; T::RowsAtCompileTime == 6,</div><div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;                <span class="stringliteral">&quot;Must have 6x1 vector&quot;</span>);</div><div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a3d70f8eb9cf1855ca989f887a5543acc">SVec&lt;typename T::Scalar&gt;</a> mv;</div><div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;  mv &lt;&lt; a(1) * b(2) - a(2) * b(1), a(2) * b(0) - a(0) * b(2),</div><div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;      a(0) * b(1) - a(1) * b(0),</div><div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;      a(1) * b(5) - a(2) * b(4) + a(4) * b(2) - a(5) * b(1),</div><div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;      a(2) * b(3) - a(0) * b(5) - a(3) * b(2) + a(5) * b(0),</div><div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;      a(0) * b(4) - a(1) * b(3) + a(3) * b(1) - a(4) * b(0);</div><div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;  <span class="keywordflow">return</span> mv;</div><div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a3d70f8eb9cf1855ca989f887a5543acc"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a3d70f8eb9cf1855ca989f887a5543acc">SVec</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 6, 1 &gt; SVec</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00062">cppTypes.h:62</a></div></div>
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          <td class="memname">auto spatial::rotationFromSXform </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>X</em></td><td>)</td>
          <td></td>
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<p>Get rotation matrix from spatial transformation </p>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00157">157</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;                                                     {</div><div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;  static_assert(T::ColsAtCompileTime == 6 &amp;&amp; T::RowsAtCompileTime == 6,</div><div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;                <span class="stringliteral">&quot;Must have 6x6 matrix&quot;</span>);</div><div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a0b83d93a3c74d282558436e26c056896">RotMat&lt;typename T::Scalar&gt;</a> R = <a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>.template topLeftCorner&lt;3, 3&gt;();</div><div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;  <span class="keywordflow">return</span> R;</div><div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;}</div><div class="ttc" id="namespaceori_html_a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">ori::CoordinateAxis::X</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a0b83d93a3c74d282558436e26c056896"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a0b83d93a3c74d282558436e26c056896">RotMat</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 3 &gt; RotMat</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00018">cppTypes.h:18</a></div></div>
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          <td class="memname"><a class="el" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a>&lt;typename T::Scalar&gt; spatial::rotInertiaOfBox </td>
          <td>(</td>
          <td class="paramtype">typename T::Scalar&#160;</td>
          <td class="paramname"><em>mass</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>dims</em>&#160;</td>
        </tr>
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<p>Construct the rotational inertia of a uniform density box with a given mass. </p><dl class="params"><dt>Parameters</dt><dd>
  <table class="params">
    <tr><td class="paramname">mass</td><td>Mass of the box </td></tr>
    <tr><td class="paramname">dims</td><td>Dimensions of the box </td></tr>
  </table>
  </dd>
</dl>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00245">245</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;                                                                         {</div><div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;  static_assert(T::ColsAtCompileTime == 1 &amp;&amp; T::RowsAtCompileTime == 3,</div><div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;                <span class="stringliteral">&quot;Must have 3x1 vector&quot;</span>);</div><div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3&lt;typename T::Scalar&gt;</a> I =</div><div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;      <a class="code" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3&lt;typename T::Scalar&gt;::Identity</a>() * dims.norm() * dims.norm();</div><div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 3; i++) I(i, i) -= dims(i) * dims(i);</div><div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;  I = I * mass / 12;</div><div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;  <span class="keywordflow">return</span> I;</div><div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_aa8cb424e643d476ea485238dad7c3e18"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 3 &gt; Mat3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00054">cppTypes.h:54</a></div></div>
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          <td class="memname"><a class="el" href="../../d9/d8e/cpp_types_8h.html#a217c4c7a22cd434b9700b183b07f1505">SXform</a>&lt;T&gt; spatial::spatialRotation </td>
          <td>(</td>
          <td class="paramtype"><a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5">CoordinateAxis</a>&#160;</td>
          <td class="paramname"><em>axis</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">T&#160;</td>
          <td class="paramname"><em>theta</em>&#160;</td>
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<p>Calculate the spatial coordinate transform from A to B where B is rotate by theta about axis. </p>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00028">28</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>

<p>References <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00060">ori::coordinateRotation()</a>, and <a class="el" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">ori::X</a>.</p>
<div class="fragment"><div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;                                                        {</div><div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;  static_assert(std::is_floating_point&lt;T&gt;::value,</div><div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;                <span class="stringliteral">&quot;must use floating point value&quot;</span>);</div><div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a0b83d93a3c74d282558436e26c056896">RotMat&lt;T&gt;</a> R = <a class="code" href="../../da/d9b/namespaceori.html#a537b8d0769c03e4cd8ef2b9a9dc8a760">coordinateRotation</a>(axis, theta);</div><div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a217c4c7a22cd434b9700b183b07f1505">SXform&lt;T&gt;</a> <a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a> = <a class="code" href="../../d9/d8e/cpp_types_8h.html#a217c4c7a22cd434b9700b183b07f1505">SXform&lt;T&gt;::Zero</a>();</div><div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;  X.template topLeftCorner&lt;3, 3&gt;() = R;</div><div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;  X.template bottomRightCorner&lt;3, 3&gt;() = R;</div><div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;  <span class="keywordflow">return</span> X;</div><div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;}</div><div class="ttc" id="namespaceori_html_a537b8d0769c03e4cd8ef2b9a9dc8a760"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a537b8d0769c03e4cd8ef2b9a9dc8a760">ori::coordinateRotation</a></div><div class="ttdeci">Mat3&lt; T &gt; coordinateRotation(CoordinateAxis axis, T theta)</div><div class="ttdef"><b>Definition:</b> <a href="../../d4/dfb/orientation__tools_8h_source.html#l00060">orientation_tools.h:60</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a217c4c7a22cd434b9700b183b07f1505"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a217c4c7a22cd434b9700b183b07f1505">SXform</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 6, 6 &gt; SXform</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00066">cppTypes.h:66</a></div></div>
<div class="ttc" id="namespaceori_html_a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">ori::CoordinateAxis::X</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a0b83d93a3c74d282558436e26c056896"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a0b83d93a3c74d282558436e26c056896">RotMat</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 3 &gt; RotMat</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00018">cppTypes.h:18</a></div></div>
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          <td class="memname">auto spatial::spatialToAngularVelocity </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>v</em></td><td>)</td>
          <td></td>
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<p>Convert from spatial velocity to angular velocity. </p>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00277">277</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;                                                           {</div><div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;  static_assert(T::ColsAtCompileTime == 1 &amp;&amp; T::RowsAtCompileTime == 6,</div><div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;                <span class="stringliteral">&quot;Must have 6x1 vector&quot;</span>);</div><div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> vsAng = v.template topLeftCorner&lt;3, 1&gt;();</div><div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;  <span class="keywordflow">return</span> vsAng;</div><div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
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          <td class="memname">auto spatial::spatialToLinearAcceleration </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>a</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T2 &gt; &amp;&#160;</td>
          <td class="paramname"><em>v</em>&#160;</td>
        </tr>
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<p>Compute the classical lienear accleeration of a frame given its spatial acceleration and velocity </p>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00289">289</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;                                                               {</div><div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;  static_assert(T::ColsAtCompileTime == 1 &amp;&amp; T::RowsAtCompileTime == 6,</div><div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;                <span class="stringliteral">&quot;Must have 6x1 vector&quot;</span>);</div><div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;  static_assert(T2::ColsAtCompileTime == 1 &amp;&amp; T2::RowsAtCompileTime == 6,</div><div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;                <span class="stringliteral">&quot;Must have 6x1 vector&quot;</span>);</div><div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;</div><div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> acc;</div><div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;  <span class="comment">// classical accleration = spatial linear acc + omega x v</span></div><div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;  acc = a.template tail&lt;3&gt;() + v.template head&lt;3&gt;().cross(v.template tail&lt;3&gt;());</div><div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;  <span class="keywordflow">return</span> acc;</div><div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
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          <td class="memname">auto spatial::spatialToLinearAcceleration </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>a</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T2 &gt; &amp;&#160;</td>
          <td class="paramname"><em>v</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T3 &gt; &amp;&#160;</td>
          <td class="paramname"><em>x</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div><div class="memdoc">
<p>Compute the classical lienear acceleration of a frame given its spatial acceleration and velocity </p>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00307">307</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>

<p>References <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00261">spatialToLinearVelocity()</a>.</p>
<div class="fragment"><div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;                                                               {</div><div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;  static_assert(T::ColsAtCompileTime == 1 &amp;&amp; T::RowsAtCompileTime == 6,</div><div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;                <span class="stringliteral">&quot;Must have 6x1 vector&quot;</span>);</div><div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;  static_assert(T2::ColsAtCompileTime == 1 &amp;&amp; T2::RowsAtCompileTime == 6,</div><div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;                <span class="stringliteral">&quot;Must have 6x1 vector&quot;</span>);</div><div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;  static_assert(T3::ColsAtCompileTime == 1 &amp;&amp; T3::RowsAtCompileTime == 3,</div><div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;                <span class="stringliteral">&quot;Must have 3x1 vector&quot;</span>);</div><div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;</div><div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> alin_x = <a class="code" href="../../de/d1a/namespacespatial.html#a95b2db654a989f56df5a8977a5be12d6">spatialToLinearVelocity</a>(a, x);</div><div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> vlin_x = <a class="code" href="../../de/d1a/namespacespatial.html#a95b2db654a989f56df5a8977a5be12d6">spatialToLinearVelocity</a>(v, x);</div><div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;</div><div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;  <span class="comment">// classical accleration = spatial linear acc + omega x v</span></div><div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> acc = alin_x + v.template head&lt;3&gt;().cross(vlin_x);</div><div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;  <span class="keywordflow">return</span> acc;</div><div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;}</div><div class="ttc" id="namespacespatial_html_a95b2db654a989f56df5a8977a5be12d6"><div class="ttname"><a href="../../de/d1a/namespacespatial.html#a95b2db654a989f56df5a8977a5be12d6">spatial::spatialToLinearVelocity</a></div><div class="ttdeci">auto spatialToLinearVelocity(const Eigen::MatrixBase&lt; T &gt; &amp;v, const Eigen::MatrixBase&lt; T2 &gt; &amp;x)</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/dc8/spatial_8h_source.html#l00261">spatial.h:261</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
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          <td class="memname">auto spatial::spatialToLinearVelocity </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>v</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T2 &gt; &amp;&#160;</td>
          <td class="paramname"><em>x</em>&#160;</td>
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<p>Convert from spatial velocity to linear velocity. Uses spatial velocity at the given point. </p>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00261">261</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>
<div class="fragment"><div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;                                                           {</div><div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;  static_assert(T::ColsAtCompileTime == 1 &amp;&amp; T::RowsAtCompileTime == 6,</div><div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;                <span class="stringliteral">&quot;Must have 6x1 vector&quot;</span>);</div><div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;  static_assert(T2::ColsAtCompileTime == 1 &amp;&amp; T2::RowsAtCompileTime == 3,</div><div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;                <span class="stringliteral">&quot;Must have 3x1 vector&quot;</span>);</div><div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> vsAng = v.template topLeftCorner&lt;3, 1&gt;();</div><div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> vsLin = v.template bottomLeftCorner&lt;3, 1&gt;();</div><div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> vLinear = vsLin + vsAng.cross(x);</div><div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;  <span class="keywordflow">return</span> vLinear;</div><div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
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          <td class="memname">auto spatial::sXFormPoint </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>X</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T2 &gt; &amp;&#160;</td>
          <td class="paramname"><em>p</em>&#160;</td>
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<p>Apply spatial transformation to a point. </p>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00329">329</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>

<p>References <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00157">rotationFromSXform()</a>, and <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00168">translationFromSXform()</a>.</p>
<div class="fragment"><div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;                                               {</div><div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;  static_assert(T::ColsAtCompileTime == 6 &amp;&amp; T::RowsAtCompileTime == 6,</div><div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;                <span class="stringliteral">&quot;Must have 6x6 vector&quot;</span>);</div><div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;  static_assert(T2::ColsAtCompileTime == 1 &amp;&amp; T2::RowsAtCompileTime == 3,</div><div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;                <span class="stringliteral">&quot;Must have 3x1 vector&quot;</span>);</div><div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;</div><div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3&lt;typename T::Scalar&gt;</a> R = <a class="code" href="../../de/d1a/namespacespatial.html#abdc3cd991206414d80d9f89be27e3633">rotationFromSXform</a>(X);</div><div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> r = <a class="code" href="../../de/d1a/namespacespatial.html#aba5e712bd3844d2e6a57dcb071f3f0a5">translationFromSXform</a>(X);</div><div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> Xp = R * (p - r);</div><div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;  <span class="keywordflow">return</span> Xp;</div><div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_aa8cb424e643d476ea485238dad7c3e18"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 3 &gt; Mat3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00054">cppTypes.h:54</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
<div class="ttc" id="namespacespatial_html_aba5e712bd3844d2e6a57dcb071f3f0a5"><div class="ttname"><a href="../../de/d1a/namespacespatial.html#aba5e712bd3844d2e6a57dcb071f3f0a5">spatial::translationFromSXform</a></div><div class="ttdeci">auto translationFromSXform(const Eigen::MatrixBase&lt; T &gt; &amp;X)</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/dc8/spatial_8h_source.html#l00168">spatial.h:168</a></div></div>
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          <td class="memname">auto spatial::sxformToHomogeneous </td>
          <td>(</td>
          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>X</em></td><td>)</td>
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<p>Convert a spatial transform to a homogeneous coordinate transformation </p>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00108">108</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>

<p>References <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00108">ori::matToSkewVec()</a>.</p>
<div class="fragment"><div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;                                                      {</div><div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;  static_assert(T::ColsAtCompileTime == 6 &amp;&amp; T::RowsAtCompileTime == 6,</div><div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;                <span class="stringliteral">&quot;Must have 6x6 matrix&quot;</span>);</div><div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a5e48cf69558cf96d92f71803cf9d19a4">Mat4&lt;typename T::Scalar&gt;</a> H = <a class="code" href="../../d9/d8e/cpp_types_8h.html#a5e48cf69558cf96d92f71803cf9d19a4">Mat4&lt;typename T::Scalar&gt;::Zero</a>();</div><div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a0b83d93a3c74d282558436e26c056896">RotMat&lt;typename T::Scalar&gt;</a> R = <a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>.template topLeftCorner&lt;3, 3&gt;();</div><div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3&lt;typename T::Scalar&gt;</a> skewR = <a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>.template bottomLeftCorner&lt;3, 3&gt;();</div><div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;  H.template topLeftCorner&lt;3, 3&gt;() = R;</div><div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;  H.template topRightCorner&lt;3, 1&gt;() = <a class="code" href="../../da/d9b/namespaceori.html#a0d9277fde185aecf3eae4a6d6450d25f">matToSkewVec</a>(skewR * R.transpose());</div><div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;  H(3, 3) = 1;</div><div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;  <span class="keywordflow">return</span> H;</div><div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_aa8cb424e643d476ea485238dad7c3e18"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#aa8cb424e643d476ea485238dad7c3e18">Mat3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 3 &gt; Mat3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00054">cppTypes.h:54</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a5e48cf69558cf96d92f71803cf9d19a4"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a5e48cf69558cf96d92f71803cf9d19a4">Mat4</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 4, 4 &gt; Mat4</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00094">cppTypes.h:94</a></div></div>
<div class="ttc" id="namespaceori_html_a0d9277fde185aecf3eae4a6d6450d25f"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a0d9277fde185aecf3eae4a6d6450d25f">ori::matToSkewVec</a></div><div class="ttdeci">Vec3&lt; typename T::Scalar &gt; matToSkewVec(const Eigen::MatrixBase&lt; T &gt; &amp;m)</div><div class="ttdef"><b>Definition:</b> <a href="../../d4/dfb/orientation__tools_8h_source.html#l00108">orientation_tools.h:108</a></div></div>
<div class="ttc" id="namespaceori_html_a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">ori::CoordinateAxis::X</a></div></div>
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template&lt;typename T &gt; </div>
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          <td class="memname">auto spatial::translationFromSXform </td>
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          <td class="paramtype">const Eigen::MatrixBase&lt; T &gt; &amp;&#160;</td>
          <td class="paramname"><em>X</em></td><td>)</td>
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<p>Get translation vector from spatial transformation </p>

<p>Definition at line <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00168">168</a> of file <a class="el" href="../../d9/dc8/spatial_8h_source.html">spatial.h</a>.</p>

<p>References <a class="el" href="../../d4/dfb/orientation__tools_8h_source.html#l00108">ori::matToSkewVec()</a>, and <a class="el" href="../../d9/dc8/spatial_8h_source.html#l00157">rotationFromSXform()</a>.</p>
<div class="fragment"><div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;                                                        {</div><div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;  static_assert(T::ColsAtCompileTime == 6 &amp;&amp; T::RowsAtCompileTime == 6,</div><div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;                <span class="stringliteral">&quot;Must have 6x6 matrix&quot;</span>);</div><div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a0b83d93a3c74d282558436e26c056896">RotMat&lt;typename T::Scalar&gt;</a> R = <a class="code" href="../../de/d1a/namespacespatial.html#abdc3cd991206414d80d9f89be27e3633">rotationFromSXform</a>(X);</div><div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;  <a class="code" href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3&lt;typename T::Scalar&gt;</a> r =</div><div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;      -<a class="code" href="../../da/d9b/namespaceori.html#a0d9277fde185aecf3eae4a6d6450d25f">matToSkewVec</a>(R.transpose() * <a class="code" href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">X</a>.template bottomLeftCorner&lt;3, 3&gt;());</div><div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;  <span class="keywordflow">return</span> r;</div><div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;}</div><div class="ttc" id="cpp_types_8h_html_a6f07728c866b15ff0676a9b2ebfd2ba6"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a6f07728c866b15ff0676a9b2ebfd2ba6">Vec3</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 1 &gt; Vec3</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00026">cppTypes.h:26</a></div></div>
<div class="ttc" id="namespaceori_html_a0d9277fde185aecf3eae4a6d6450d25f"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a0d9277fde185aecf3eae4a6d6450d25f">ori::matToSkewVec</a></div><div class="ttdeci">Vec3&lt; typename T::Scalar &gt; matToSkewVec(const Eigen::MatrixBase&lt; T &gt; &amp;m)</div><div class="ttdef"><b>Definition:</b> <a href="../../d4/dfb/orientation__tools_8h_source.html#l00108">orientation_tools.h:108</a></div></div>
<div class="ttc" id="namespaceori_html_a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383"><div class="ttname"><a href="../../da/d9b/namespaceori.html#a02c20a1b1d35988c657aa1e219d609d5a02129bb861061d1a052c592e2dc6b383">ori::CoordinateAxis::X</a></div></div>
<div class="ttc" id="cpp_types_8h_html_a0b83d93a3c74d282558436e26c056896"><div class="ttname"><a href="../../d9/d8e/cpp_types_8h.html#a0b83d93a3c74d282558436e26c056896">RotMat</a></div><div class="ttdeci">typename Eigen::Matrix&lt; T, 3, 3 &gt; RotMat</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/d8e/cpp_types_8h_source.html#l00018">cppTypes.h:18</a></div></div>
<div class="ttc" id="namespacespatial_html_abdc3cd991206414d80d9f89be27e3633"><div class="ttname"><a href="../../de/d1a/namespacespatial.html#abdc3cd991206414d80d9f89be27e3633">spatial::rotationFromSXform</a></div><div class="ttdeci">auto rotationFromSXform(const Eigen::MatrixBase&lt; T &gt; &amp;X)</div><div class="ttdef"><b>Definition:</b> <a href="../../d9/dc8/spatial_8h_source.html#l00157">spatial.h:157</a></div></div>
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